Question: Simplify the following expression and state the condition under which the simplification is valid: $n = \dfrac{r^2 - 8r}{r^2 - 5r - 24}$
Solution: First factor the expressions in the numerator and denominator. $ \dfrac{r^2 - 8r}{r^2 - 5r - 24} = \dfrac{(r)(r - 8)}{(r + 3)(r - 8)} $ Notice that the term $(r - 8)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(r - 8)$ gives: $n = \dfrac{r}{r + 3}$ Since we divided by $(r - 8)$, $r \neq 8$. $n = \dfrac{r}{r + 3}; \space r \neq 8$